Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
516 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14545714 | C2 | semidirect |
| 2. #14544917 | C2 | semidirect |
| 3. C4×#10587550 | C2 | semidirect |
| 4. #14544105 | C2 | semidirect |
| 5. #14543670 | C2 | semidirect |
| 6. #14543611 | C2 | semidirect |
| 25. #11763096 | C4 | semidirect |
| 26. #11763009 | C4 | semidirect |
| 27. #11763005 | C4 | semidirect |
| 32. C17×#477 | C4 | semidirect |
| 167. D68 | #104 | semidirect |
| 221. #477 | #595 | semidirect |
| 299. C17 | #8969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545714 | 2 |
| #14544917 | 2 |
| C4×#10587550 | 2 |
| #14544105 | 2 |
| #14543670 | 2 |
| #14543611 | 2 |
| #14538847 | 2 |
| #8969 | 17 |